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Nitrogen atom diffusion into TiO2 anatase bulk via surfaces
Computational Materials Science 82 (2014) 107–113
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Nitrogen atom diffusion into TiO2 anatase bulk via surfaces Xuan Hu a, Rui Tu a, Jianhong Wei a, Chunxu Pan a, Jindong Guo c, Wei Xiao a,b,⇑ a
Department of Physics, Wuhan University, Wuhan 430072, PR China State Nuclear Power Research Institute, Beijing 100029, PR China c State Nuclear Power Engineering Company Ltd., Shanghai 200233, PR China b
a r t i c l e
i n f o
Article history: Received 30 April 2013 Accepted 14 September 2013 Available online 15 October 2013 Keywords: TiO2 anatase Nitrogen Diffusion Interstitial Surface First principles Adsorption Nudged elastic band method
a b s t r a c t Nitrogen atom diffusion from anatase surfaces to the bulk via the interstitial sites is studied by first principle calculations and nudged elastic band method. Anatase surfaces (1 0 1), (0 0 1), (1 0 0), and (1 0 3) are chosen for the surface diffusion calculations. It shows that the diffusion from the outermost surface to the sub-surface is the most difficult step for a N atom diffusing into the bulk and it is easier for a N atom diffusing out of the bulk and staying on the surface or at the sub-surface sites. According to the diffusion barriers, N diffusion into the bulk via a (1 0 1) surface is relatively easier than the diffusion via other three surfaces for the N doping process. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Since 1970s, TiO2 was used as a photo-catalyst to decompose water by Fujishima and Honda [1], TiO2 became a popular material and attracted many scientific interests. With its unique chemical and physical properties, TiO2 has been widely used in many fields, like solar cell and photo-catalyst [2,3]. Because the bandwidth of anatase is 3.2 eV, TiO2 can only absorb ultraviolet with wavelength below 387 nm. The photon absorption efficiency is very low. Various methods have been developed to improve its efficiency as a photo-catalyst [4–8]. In order to overcome this problem, Asahi group studied the doping effect on the photon adsorption property of TiO2 with first principle calculations [9]. C, F, N, P and other nonmetal elements were chosen as the dopants and it was found that N-doped TiO2 can change the bandwidth dramatically and it can be used to improve the photon absorption efficiency. From then on, various preparation methods for N-doped TiO2 have been developed and their properties have been studied intensively [10–21]. Although many experimental works have been done, the fundamental mechanism for the N doping process is not clear yet. In this paper, first-principle calculations and nudged elastic band (NEB) method are used to simulate an interstitial N atom diffusing into the bulk from four anatase surfaces. The energy barriers for N atom diffusion from the outermost surfaces to the subsurface ⇑ Corresponding author at: Department of Physics, Wuhan University, Wuhan 430072, PR China. Tel.: +86-189-7122-0896; fax: +86 27 6875 2003. E-mail address: [email protected] (W. Xiao). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.09.028
sites are the most difficult steps. It is relatively easier for a N atom diffusing out of the bulk to the surfaces. As a result, the concentration of N doping atom on the surface or at the sub-surface area is higher than that of the bulk. In the four surfaces we studied, anatase (1 0 1) is the surface from which N atom can diffuse into the bulk relatively easier via interstitial sites. 2. Computational methods and Simulation models 2.1. Computational methods The density functional theory (DFT) calculations [22,23] are performed to calculate the ground state energies of the systems and the energy calculations are performed with the Vienna ab initio simulation package (VASP) code [24,25]. The projected augmented wave (PAW) method [26,27] is used to deal with the wave functions near the core region. The exchange correlation functional within the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Enzerof (PBE) [28,29] is used in the calculations. The cutoff of the plane-wave kinetic energy is 400 eV. In the energy calculations for the structure relaxation and the diffusion path search, the summations over the Brillouin zone are performed with a 4 4 1 MonkhorstPack k-point mesh for the surface calculations, and a 2 2 2 k-point mesh for the bulk calculations. In the electronic relaxation calculations, the residual minimization method with direct inversion in the iterative subspace (RMM-DIIS) [30,31] is used and the energy convergence criterion is 104 eV. The conjugate gradient method is used to
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minimize the Hellmann–Feynman forces in the ionic relaxations with the force stopping criterion of 0.05 eV/Å. Spin-polarization is used in all calculations. The climb image nudged elastic band (CI-NEB) method [32–34] is used to search the minimal energy paths and the saddle points of a N atom diffusion near the anatase surfaces. The VTST code [35] combined with VASP is performed in the diffusion calculations. The quick-min method (QM) is used to relax the NEB forces. In most of the NEB calculations, there are four images between the initial and final configurations. In some cases, eight images are used. The spring constant of the NEB calculations is 5.0 eV/Å2 and the force convergence criteria is 0.05 eV/Å. For an interstitial N atom in an anatase slab, the interstitial formation energy is defined as:
EðNi Þ ¼ Eðslab þ Ni Þ EðslabÞ EðNÞ
ð1Þ
here, E(slab + Ni), E(slab), and E(N) are the energies of the TiO2 slab with an interstitial N atom, the relaxed bare slab, and a single N atom, respectively. In our calculations, the bottom part of the super cell is fixed and the upper part is free to relax. The surface energy is calculated as follow. Suppose a super cell is cut from a solid and two surfaces are formed if we keep the periodic bondary condition in x and y
direction. Without relaxation, the energy change of the system is 2Ed and the surface area is A. If we relax the super cell, the system energy decrease further and the energy change is 2Er. The surface energy can be defined as,
Esurf ¼ ðEd þ Er Þ=A:
ð2Þ
If one surface is fixed, the energy change of the super cell is:
EðunrelaxedÞ EðbulkÞ ¼ 2Ed
ð3Þ
EðslabÞ EðbulkÞ ¼ Ed þ ðEd þ Er Þ
ð4Þ
here, E(unrelaxed), E(slab), E(bulk) are energy of the unrelaxed slab, the energy of the relaxed slab, and the energy of corresponding slab in the bulk, respectively. Plug in Eqs. (3) and (4) into Eq. (2) and the surface energy is
1 1 A: Esurf ¼ EðslabÞ EðbulkÞ EðunrelaxedÞ 2 2
ð5Þ
2.2. Simulation model for N-doped anatase surfaces With the PBE pseudopotential, our optimized lattice parameters for the body-centered tetragonal (bct) bulk anatase are a = 3.83 Å
Fig. 1. The surface structures used to simulate anatase (0 0 1), (1 0 0), (1 0 1), and (1 0 3) surfaces. They are used for the N atom diffusion calculations. The numbers in the picture represent different oxygen sites. The large gray circles represent Ti atoms and small red circles are O atoms. (a) super cell for (1 0 1) slab with 4(6) structure layers and a 2 2 (2 2) surface. (b) super cell for (0 0 1) slab with 3(6) structure layers and a 2 3 (2 2) surface. (c) super cell for (1 0 0) slab with 4(6) structure layers and a 2 1 (2 1) surface. (d) super cell for (1 0 3) slab with 6(6) structure layers and a 2 2 (2 1) surface. In order to show the structure clearly, less layers and larger surface area are shown in the figures. The data in the brackets is the real parameters used in this work. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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and c = 9.62 Å. They agree with experimental data (a = 3.78 Å and c = 9.51 Å) [36] well. Four super cells are used to simulate anatase (1 0 1), (0 0 1), (1 0 0), and (1 0 3) surface diffusion (see Fig. 1). Each slab has six repeating stoichiometric (TiO2) structure layers and each layer has four Ti atoms and eight O atoms. The atomic coordinates of the two bottom layers are fixed and the other four layers are free to relax. A vacuum layer on the top of the surface of each super cell is used to eliminate the interaction between the neighbor slabs since the periodic boundary condition is applied. The computational parameters of the super cells are listed in Table 1. Two types of vacuum layer are selected to calculate the surface energies (see Table 1). Although the thickness of the vacuum layer B is larger than that of the layer A, the surface energies for both structures are very similar. As a result, vacuum type A is selected to study the surface diffusion since it can reduce the computational time. Our surface energies are close to the data from other literature [37]. The sequence of our calculated surface energies for different surfaces is: Es(1 0 1) < Es(1 0 0) < Es(1 0 3) < Es(0 0 1). It suggests that anatase (1 0 1) surface is the most stable one and the anatase (0 0 1) surface is the most active one. This
conclusion agrees with the results from other research groups [37,38]. 3. A nitrogen interstitial atom diffusion in bulk anatase 3.1. Configurations of N interstitial atom in bulk anatase Because the formation energy for a N interstitial atom is lower than that for a N substitutional atom [39], a N atom diffusion via the interstitial sites is studied in this work. Three N atom interstitial configurations are found in the bulk anatase and they are shown in Fig. 2. The formation energies of the three types of interstitial configuration (in a 108 + 1 atom super cell) are: 1.145 eV (type 1), 1.007 eV (type 2), 0.577 eV (type 3). It suggests that the interstitial configuration type 1 is the most stable one in the three configurations. Consequently, interstitial configuration type 1 is mainly studied in this work. 3.2. N atom diffusion in bulk anatase All of the Ti atoms in the anatase bulk material are equivalent. One Ti atom in the bulk anatase has six neighbor O atoms. This TiO6
Table 1 Computational parameters used for the bulk and surface calculation. Es represents surface energy of a super cell. For bulk calculation, a 12 atom cell is used for the total energy calculation, a 108 atom cell is used for energy analysis, and a 48 atom cell is used for the bulk diffusion calculation. Bulk
Surfaces (1 0 1)
Atom number Structure layer Mesh of k points Surface periodicity Vacuum thickness A (Å) Vacuum thickness B (Å) Slab thickness (Å) Surface areas (Å2)
12/48/108 – 222 – – – – –
Es (A) (J/m2) Es (B) (J/m2) Es (J/m2) [37]
– – –
72 6 441 22 8.9 10 10.7 79.4 0.50 0.50 0.49
(0 0 1) 72 6 441 22 8.6 10 14.4 58.8 0.97 0.96 0.98
(1 0 0) 72 6 441 21 9.6 11 11.5 73.8 0.57 0.56 0.58
(1 0 3) 72 6 441 21 9.8 11 14.8 57.5 0.91 0.90 0.90
Fig. 2. Three configurations for a N interstitial atom in bulk anatase. The upper figures are the top view of the configurations and the the bottom ones are the side view. The gray circles represent Ti atoms, the red ones are O atoms, and the blue one is the N interstitial atom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Possible diffusion paths in bulk anatase.
unit is a distorted octahedron structure. Since in the interstitial type 1, the N atom shares one site with an oxygen atom, the N interstitial atom can diffuse from one oxygen site to another neighbor equivelent site. Due to the symmetry, there are three different O–O edges in one TiO6 octahedron structure (see Fig. 3). For example, the N interstitial atom can diffuse along three edges, the path A, B, and C in Fig. 3. The three diffusion paths and corresponding energy barriers for a N atom diffusion along three different edges are shown in Fig. 4. The diffusion barrier for the three paths are: EA = 1.43 eV, EC = 1.83 eV, and EB = 1.94 eV. In these three paths, the energy barrier for path A is at least 0.4 eV lower than that of path C and path B. Consequently, the N interstitial atom diffusion along path A is relatively easier than the diffusion along the other two directions. If an interstitial N atom diffuses in the bulk anatase continuously along a series of path A, the N atom can travel in the solid. With the combination of a series of path A, the N atom can diffuse in the direction of [1 0 0] and [0 1 0] (see Fig. 5) along the zigzag paths. Since an interstitial site is close to an oxygen atom, the zigzag path is represented by the connection of a series of oxygen atoms in Fig. 5. The interstitial N atom can diffuse in the direction of [1 0 0] and [0 1 0] with the diffusion barrier of 1.43 eV. With the combination of the two directions, the N atom can travel in the bulk anatase.
Fig. 5. Multiple diffusion steps of an interstitial N atom in TiO2 anatase solid along the type A path in Fig. 4.
4. N atom diffusion into the anatase surfaces 4.1. Formation energies of a N interstitial atom near the anatase surfaces In bulk anatase, a N interstitial atom stays at a position in the type 1 configuration (see Fig. 2). Near the surface area, serious configuration distortion happens after relaxation due to the interstitial atom. The N interstitial atom formation energies near the anatase surface area are listed in Table 2. In this table, a subscript ‘o’ is used for the serious distorted interstitial configurations. Super cells in Fig. 1 are used to study the N atom diffusion into the anatase surfaces. The interstitial sites studied in this work in each cell are denoted as ‘‘1, 2, 3, . . . ’’ in Fig. 1 and ‘‘O1, O2, O3, . . .’’ in Table 2. The data in Table 2 shows that the formation energy for a N interstitial atom increases with the depth, that is the distance from the interstitial atom to the surface. It suggests that it is difficult for an interstitial N atom diffusing into the deeper sites from the surfaces. In the super cells for (1 0 0) and (1 0 1) surface calculations, the interstitial formation energies at deep sites are close to that of the bulk, which is 1.145 eV. So, the surface effect is mainly located at the top two or three structure layers. When a N atom diffuses into deep sites, the environment for this atom is close to that of the bulk. For the N atom diffusing into the bulk from a surface, it
(b) (a)
Fig. 4. (a) Three non-equivalent diffusion paths along the three edges of the distorted octahedron in Fig. 3. (b) Diffusion barriers for the three diffusion paths. The Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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X. Hu et al. / Computational Materials Science 82 (2014) 107–113 Table 2 The formation energies of a N interstitial atom near the anatase surfaces. Subscript ‘o’ means serious configuration distortion happens after relaxation for the N interstitial structure. The unit of energy is eV. (1 0 1)
(0 0 1)
(1 0 0)
(1 0 3)
Site
Energy
Site
Energy
Site
Energy
Site
Energy
O7(o) O2(o) O3(o) O4 O1 O5 O6
2.714 2.074 1.564 1.503 1.147 1.143 1.120
O2(o) O1(o) O5 O6 O3 O4
3.199 1.933 1.093 0.918 0.916 0.741
O1(o) O2(o) O5 O3 O6 O4
2.553 2.293 1.402 1.236 1.211 1.178
O2(o) O8(o) O9(o) O1(o) O5 O4 O7 O10 O6 O3
3.249 2.935 2.154 1.987 1.250 1.222 1.213 1.097 1.089 0.912
has to go cross the outmost surface regime (about two or three structure layers) and then go into the bulk. The diffusion paths and corresponding barriers for different surfaces are different. Consequently, the surface diffusion barriers for a N atom is interesting and the diffusion barriers for different surfaces can tell us which surface is the better one for the N doping processes. 4.2. A nitrogen atom diffusing into the bulk from anatase (1 0 1) surface via interstitial sites Nitrogen interstitial atom diffusion into the bulk from an anatase (1 0 1) surface is studied in this section. The super cell used to simulate the diffusion process is shown in Fig. 1(a). Since a N interstitial atom share a lattice with an oxygen atom, the position of the oxygen atoms are used to describe the possible interstitial position in the super cell. In this super cell, the site 2, 3, and 7 are at the outermost surface of the super cell. Interstitial site 1 is a subsurface site. Site 4, 5, and 6 are at even deeper position in the super cell. The process of a nitrogen atom diffusing into the bulk from the surface is studied and the diffusion barriers are listed in Table 3. The following diffusion paths have been calculated: O2 ? O4 (from the interstitial site O2 to site O4); O3 ? O4; {O2, O3, O7} ? O1, it means the N interstitial atom can diffuse from O2, O3, or O7 to O1 position; O1 ? {O4n, O5, O6} (O4n is an O4 site in the next period along x axes). These diffusion paths and barriers show us how a nitrogen atom diffuses into the bulk from a (1 0 1) anatase surface. Energy barriers for the (1 0 1) surface diffusion are shown in Table 3. In these paths, the barrier for O3 ? O4 is the lowest one, which is 1.80 eV. The configuration and the barrier for this path is close to the diffusion path C in the bulk (see Fig. 4). The barrier is higher than that of the path A in the bulk. Although a N interstitial atom can diffuse from O2, O3, or O7 to O1 site and then diffuse to O4, the barriers for the interstitial atom diffusing to the O1 site are much higher and they are not efficient diffusion pathways. As a
Table 3 Energy barriers for a N interstitial atom diffusing into the bulk from the (1 0 1) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier.
Fig. 6. Schematic of a N interstitial atom diffusing from site O3 to site O4 in (1 0 1) direction. The configurations of O3, O4, and the transition state are shown in the figure. Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atom is the blue one. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
result, a N interstitial atom can most likely diffuse from the pathway O3 ? O4 (see Fig. 6). For this diffusion path, the barrier is very close to the reverse diffusion barrier. Meanwhile, if a N atom diffuses to the O1 site from the surface, the reverse barriers are much lower than the counterparts. It suggests that the N atom may diffuse outside from these diffusion pathways. 4.3. A nitrogen atom diffusing into the bulk from anatase (0 0 1) surface via interstitial sites In the super cell for (0 0 1) surface diffusion calculation (see Fig. 1), sites 1 and 2 are on the outermost surface, sites 3 and 4 are the sub-surface interstitial positions, sites 5 and 6 are in the bulk. Three paths are used to study the N interstitial from the outermost surface to the sub-surface site: O1 ? O3, O1 ? O4, and O2 ? O4. Since the system energy difference for the configuration O2 and O4 is 2.44 eV, the barrier will be higher than that. The barrier for this path will be too high to be useful. For the path O1 ? O4, there is a local minimal O4a, this path can be separated into two parts: O1 ? O4a, O4a ? O4. From the subsurface to the bulk, there are three paths are studied: O3 ? O5, O3 ? O6, and O4 ? O6. The diffusion barriers are listed in Table 4. The schematic of the diffusion path O1 ? O4 ? O6 is shown in Fig. 7. The highest energy barrier is 2.28 eV in this path, which is higher than the barrier of mode A, B, and C in bulk. The first barrier is still higher than the next step and a N interstitial atom will diffuse outside easier. How a N interstitial atom diffuses into the subsurface from the outermost surface is the most difficult step for the doping process. 4.4. A nitrogen atom diffusing into the bulk from anatase (1 0 0) surface via interstitial sites In the super cell for (1 0 0) surface diffusion calculation (see Fig. 1), the sites 1 and 2 are on the surface, the sites 3 and 4 are
Table 4 Diffusion barriers for a nitrogen atom into the bulk from a (0 0 1) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier for a diffusion process.
Path
Eb1 (eV)
Eb2 (eV)
O2 ? O4 O3 ? O4
2.72 1.80
2.15 1.74
Path
Eb1 (eV)
Eb2 (eV)
O2 ? O1 O3 ? O1 O7 ? O1
2.78 2.48 2.95
1.85 2.06 1.38
O1 ? O3 O1 ? O4a O4a ? O4
2.71 2.28 0.40
1.69 1.31 0.10
O1 ? O4n O1 ? O5 O1 ? O6
1.57 1.89 2.17
1.70 1.88 2.15
O3 ? O5 O3 ? O6 O4 ? O6
1.76 0.83 1.78
1.94 0.83 1.96
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Fig. 7. Schematic of a N interstitial atom diffusion via path O1 ? O4 ? O6 on an anatase (0 0 1) surface. The configurations of O1, O4, O6, and the transition states are shown in the figure. Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
at sub-surface position, and the sites 5 and 6 are in the bulk. The diffusion barriers for six paths are calculated and they are listed in Table 5. The barriers for the paths O1 ? O4, O1 ? O3, and O2 ? O4 are higher than 2.38 eV. Meanwhile, the barriers for the paths O4 ? O5, O3s ? O5, O4 ? O6 are lower than 1.80 eV. Near site O3, there is a local minimal in the path O3 ? O5. Since the barrier of the diffusion O3 ? O3s is very low, the barrier of the path O3s ? O5 is used to evaluate the barrier of O3 ? O5. It suggests that if a nitrogen atom diffuses into the bulk from a (1 0 0) surface, the first step is more difficult than the second step since the barriers of the first step are higher than that of the second step and the barrier of bulk diffusion. In the first step, the barriers are much lower than that of the reverse barriers. As a result, for the N doping process via (1 0 0) surface, the outermost diffusion step is the most difficult. On the other hand, the N interstitial will diffuse outside to the surface easily. The schematic of the diffusion path O1 ? O4 ? O5 is shown in Fig. 8. For the second step, the barriers are lower than that of the reverse barriers. So, once a N atom diffuses to a subsurface Table 5 Diffusion barriers for a nitrogen atom diffusion into the bulk from a (1 0 0) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier for a diffusion process. Path
Eb1 (eV)
Eb2 (eV)
O1 ? O4 O1 ? O3 O2 ? O4
2.38 2.74 2.71
1.01 1.43 1.60
O4 ? O5 O3s ? O5 O4 ? O6
1.06 1.62 1.76
1.28 1.72 1.89
position, it is relatively easy for this atom to diffuse to the bulk. For example, if a N atom is at the site O4, the barrier for the diffusion process O4 ? O1 is 1.01 eV, and the barrier for the path O4 ? O5 is 1.06 eV. The possibilities for both side diffusion are almost the same. Once a N atom at site O4 diffuses to site O5, the reverse barrier will be higher. It can continue to diffuse into the bulk. 4.5. A nitrogen atom diffusing into the bulk from anatase (1 0 3) surface via interstitial sites In the super cell for (1 0 3) surface diffusion calculation (see Fig. 1), the sites 2 and 8 are on the outermost surface, sites 1, 3, and 9 are for the sub-surface interstitial, sites 4, 5, 6, 7, and 10 are in the bulk. Two diffusion paths are studied for the surface to subsurface diffusion: O2 ? O1 and O8 ? O9. Four paths are chosen to describe how a nitrogen interstitial atom diffuses from a sub-surface site to the bulk: O1 ? O7, O1 ? O10, O9 ? O4, and O9 ? O5.
Table 6 Energy barriers for a N interstitial atom diffusing into an anatase (1 0 3) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier. Path
Eb1 (eV)
Eb2 (eV)
O2 ? O1 O8 ? O8a O8a ? O9a O9a ? O9
2.41 1.11 2.15 0.48
1.15 0.61 1.36 1.00
O1 ? O7 O1 ? O10 O9 ? O4 O9 ? O5a
2.66 2.43 2.29 2.69
1.89 1.31 1.35 1.79
Fig. 8. The schematic of a N atom diffusing into the bulk via a (1 0 0) surface. The diffusion path is O1 ? O4 ? O5. Three interstitial sites and two transition states (TS) are shown in the picture. The Ti atoms are the gray circles, O atoms are the red ones, the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
X. Hu et al. / Computational Materials Science 82 (2014) 107–113
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Fig. 9. The schematic of a N atom diffusing into the bulk from a (1 0 3) surface. The diffusion path is O8 ? O9 ? O4. Three interstitial sites and two transition states (TS) are shown in the picture. The Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The diffusion barriers for these paths from NEB calculations are listed in Table 6. When we calculated the N interstitial diffusion via the path O8 ? O9, two local minimal configurations are found, O8a and O9a. From the diffusion barrier table, it shows that the highest barrier is 2.15 eV for this path, which is much higher than the diffusion barrier in the bulk. Similarly, the barriers are higher than the reverse barrier for the partial diffusion O8a ? O9a. The barrier for the path O2 ? O1 is 2.41 eV and it is also higher than the reverse barrier. So, a nitrogen atom diffusing into the bulk from the outermost surface is also difficult via a (1 0 3) surface. Once a nitrogen atom is at the subsurface position of a (1 0 3) surface, it can continue to diffuse to next step towards the bulk. For this step, the barriers are also higher than 2 eV and they are much higher than the corresponding reverse barriers (see Table 6). As a result, when a nitrogen atom diffuses from an outermost (1 0 3) surface, the first two steps are difficult and the N atom prefers to diffuse out of the surface. The schematic of a N atom multiple step diffusion from a (1 0 3) surface is shown in Fig. 9. The diffusion path O8 ? O9 ? O4. It seems N atom diffusion into the bulk via an (1 0 3) surface is more difficult than the reverse diffusion. 5. Conclusions For N interstitial atom diffusion in anatase bulk, the N atom may diffuse in two directions: [1 0 0]-Z path and [0 1 0]-Z path or combination of the two directions (see Fig. 5). From the surface diffusion barrier calculations, for a N interstitial atom diffusion from the outermost surface to bulk, how a N atom diffusing from the outermost surface to the sub-surface is the most difficult step. For the four surfaces we have studied, the sequence for the highest barriers for each surface is: (1 0 1) (1.80 eV) < (0 0 1) (2.28 eV) (1 0 3) (2.29 eV) < (1 0 0) (2.38 eV). It suggests that (1 0 1) surface may be the easiest one for us to dope N atom to anatase bulk from the surfaces. The (1 0 0) surface is the relatively difficult one. Meanwhile, N interstitial atoms can diffuse to the surface from the bulk easier than the diffusion in the opposite direction. Another conclusion is that if we have already synthesized some N-doped anatase particles or bulk materials, the N doping concentration near the surfaces is higher than that of the bulk. Acknowledgments This work is supported by the Chinese National Basic Research Program (973 Program) Project 2009CB939705 and the Chinese
National Science Foundation Project 10704058. One author acknowledges the World Class University (WCU) program Grant No. R31-2010-000-10083-0 of the Korea Research Foundation. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Nitrogen atom diffusion into TiO2 anatase bulk via surfaces Xuan Hu a, Rui Tu a, Jianhong Wei a, Chunxu Pan a, Jindong Guo c, Wei Xiao a,b,⇑ a
Department of Physics, Wuhan University, Wuhan 430072, PR China State Nuclear Power Research Institute, Beijing 100029, PR China c State Nuclear Power Engineering Company Ltd., Shanghai 200233, PR China b
a r t i c l e
i n f o
Article history: Received 30 April 2013 Accepted 14 September 2013 Available online 15 October 2013 Keywords: TiO2 anatase Nitrogen Diffusion Interstitial Surface First principles Adsorption Nudged elastic band method
a b s t r a c t Nitrogen atom diffusion from anatase surfaces to the bulk via the interstitial sites is studied by first principle calculations and nudged elastic band method. Anatase surfaces (1 0 1), (0 0 1), (1 0 0), and (1 0 3) are chosen for the surface diffusion calculations. It shows that the diffusion from the outermost surface to the sub-surface is the most difficult step for a N atom diffusing into the bulk and it is easier for a N atom diffusing out of the bulk and staying on the surface or at the sub-surface sites. According to the diffusion barriers, N diffusion into the bulk via a (1 0 1) surface is relatively easier than the diffusion via other three surfaces for the N doping process. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Since 1970s, TiO2 was used as a photo-catalyst to decompose water by Fujishima and Honda [1], TiO2 became a popular material and attracted many scientific interests. With its unique chemical and physical properties, TiO2 has been widely used in many fields, like solar cell and photo-catalyst [2,3]. Because the bandwidth of anatase is 3.2 eV, TiO2 can only absorb ultraviolet with wavelength below 387 nm. The photon absorption efficiency is very low. Various methods have been developed to improve its efficiency as a photo-catalyst [4–8]. In order to overcome this problem, Asahi group studied the doping effect on the photon adsorption property of TiO2 with first principle calculations [9]. C, F, N, P and other nonmetal elements were chosen as the dopants and it was found that N-doped TiO2 can change the bandwidth dramatically and it can be used to improve the photon absorption efficiency. From then on, various preparation methods for N-doped TiO2 have been developed and their properties have been studied intensively [10–21]. Although many experimental works have been done, the fundamental mechanism for the N doping process is not clear yet. In this paper, first-principle calculations and nudged elastic band (NEB) method are used to simulate an interstitial N atom diffusing into the bulk from four anatase surfaces. The energy barriers for N atom diffusion from the outermost surfaces to the subsurface ⇑ Corresponding author at: Department of Physics, Wuhan University, Wuhan 430072, PR China. Tel.: +86-189-7122-0896; fax: +86 27 6875 2003. E-mail address: [email protected] (W. Xiao). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.09.028
sites are the most difficult steps. It is relatively easier for a N atom diffusing out of the bulk to the surfaces. As a result, the concentration of N doping atom on the surface or at the sub-surface area is higher than that of the bulk. In the four surfaces we studied, anatase (1 0 1) is the surface from which N atom can diffuse into the bulk relatively easier via interstitial sites. 2. Computational methods and Simulation models 2.1. Computational methods The density functional theory (DFT) calculations [22,23] are performed to calculate the ground state energies of the systems and the energy calculations are performed with the Vienna ab initio simulation package (VASP) code [24,25]. The projected augmented wave (PAW) method [26,27] is used to deal with the wave functions near the core region. The exchange correlation functional within the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Enzerof (PBE) [28,29] is used in the calculations. The cutoff of the plane-wave kinetic energy is 400 eV. In the energy calculations for the structure relaxation and the diffusion path search, the summations over the Brillouin zone are performed with a 4 4 1 MonkhorstPack k-point mesh for the surface calculations, and a 2 2 2 k-point mesh for the bulk calculations. In the electronic relaxation calculations, the residual minimization method with direct inversion in the iterative subspace (RMM-DIIS) [30,31] is used and the energy convergence criterion is 104 eV. The conjugate gradient method is used to
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minimize the Hellmann–Feynman forces in the ionic relaxations with the force stopping criterion of 0.05 eV/Å. Spin-polarization is used in all calculations. The climb image nudged elastic band (CI-NEB) method [32–34] is used to search the minimal energy paths and the saddle points of a N atom diffusion near the anatase surfaces. The VTST code [35] combined with VASP is performed in the diffusion calculations. The quick-min method (QM) is used to relax the NEB forces. In most of the NEB calculations, there are four images between the initial and final configurations. In some cases, eight images are used. The spring constant of the NEB calculations is 5.0 eV/Å2 and the force convergence criteria is 0.05 eV/Å. For an interstitial N atom in an anatase slab, the interstitial formation energy is defined as:
EðNi Þ ¼ Eðslab þ Ni Þ EðslabÞ EðNÞ
ð1Þ
here, E(slab + Ni), E(slab), and E(N) are the energies of the TiO2 slab with an interstitial N atom, the relaxed bare slab, and a single N atom, respectively. In our calculations, the bottom part of the super cell is fixed and the upper part is free to relax. The surface energy is calculated as follow. Suppose a super cell is cut from a solid and two surfaces are formed if we keep the periodic bondary condition in x and y
direction. Without relaxation, the energy change of the system is 2Ed and the surface area is A. If we relax the super cell, the system energy decrease further and the energy change is 2Er. The surface energy can be defined as,
Esurf ¼ ðEd þ Er Þ=A:
ð2Þ
If one surface is fixed, the energy change of the super cell is:
EðunrelaxedÞ EðbulkÞ ¼ 2Ed
ð3Þ
EðslabÞ EðbulkÞ ¼ Ed þ ðEd þ Er Þ
ð4Þ
here, E(unrelaxed), E(slab), E(bulk) are energy of the unrelaxed slab, the energy of the relaxed slab, and the energy of corresponding slab in the bulk, respectively. Plug in Eqs. (3) and (4) into Eq. (2) and the surface energy is
1 1 A: Esurf ¼ EðslabÞ EðbulkÞ EðunrelaxedÞ 2 2
ð5Þ
2.2. Simulation model for N-doped anatase surfaces With the PBE pseudopotential, our optimized lattice parameters for the body-centered tetragonal (bct) bulk anatase are a = 3.83 Å
Fig. 1. The surface structures used to simulate anatase (0 0 1), (1 0 0), (1 0 1), and (1 0 3) surfaces. They are used for the N atom diffusion calculations. The numbers in the picture represent different oxygen sites. The large gray circles represent Ti atoms and small red circles are O atoms. (a) super cell for (1 0 1) slab with 4(6) structure layers and a 2 2 (2 2) surface. (b) super cell for (0 0 1) slab with 3(6) structure layers and a 2 3 (2 2) surface. (c) super cell for (1 0 0) slab with 4(6) structure layers and a 2 1 (2 1) surface. (d) super cell for (1 0 3) slab with 6(6) structure layers and a 2 2 (2 1) surface. In order to show the structure clearly, less layers and larger surface area are shown in the figures. The data in the brackets is the real parameters used in this work. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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and c = 9.62 Å. They agree with experimental data (a = 3.78 Å and c = 9.51 Å) [36] well. Four super cells are used to simulate anatase (1 0 1), (0 0 1), (1 0 0), and (1 0 3) surface diffusion (see Fig. 1). Each slab has six repeating stoichiometric (TiO2) structure layers and each layer has four Ti atoms and eight O atoms. The atomic coordinates of the two bottom layers are fixed and the other four layers are free to relax. A vacuum layer on the top of the surface of each super cell is used to eliminate the interaction between the neighbor slabs since the periodic boundary condition is applied. The computational parameters of the super cells are listed in Table 1. Two types of vacuum layer are selected to calculate the surface energies (see Table 1). Although the thickness of the vacuum layer B is larger than that of the layer A, the surface energies for both structures are very similar. As a result, vacuum type A is selected to study the surface diffusion since it can reduce the computational time. Our surface energies are close to the data from other literature [37]. The sequence of our calculated surface energies for different surfaces is: Es(1 0 1) < Es(1 0 0) < Es(1 0 3) < Es(0 0 1). It suggests that anatase (1 0 1) surface is the most stable one and the anatase (0 0 1) surface is the most active one. This
conclusion agrees with the results from other research groups [37,38]. 3. A nitrogen interstitial atom diffusion in bulk anatase 3.1. Configurations of N interstitial atom in bulk anatase Because the formation energy for a N interstitial atom is lower than that for a N substitutional atom [39], a N atom diffusion via the interstitial sites is studied in this work. Three N atom interstitial configurations are found in the bulk anatase and they are shown in Fig. 2. The formation energies of the three types of interstitial configuration (in a 108 + 1 atom super cell) are: 1.145 eV (type 1), 1.007 eV (type 2), 0.577 eV (type 3). It suggests that the interstitial configuration type 1 is the most stable one in the three configurations. Consequently, interstitial configuration type 1 is mainly studied in this work. 3.2. N atom diffusion in bulk anatase All of the Ti atoms in the anatase bulk material are equivalent. One Ti atom in the bulk anatase has six neighbor O atoms. This TiO6
Table 1 Computational parameters used for the bulk and surface calculation. Es represents surface energy of a super cell. For bulk calculation, a 12 atom cell is used for the total energy calculation, a 108 atom cell is used for energy analysis, and a 48 atom cell is used for the bulk diffusion calculation. Bulk
Surfaces (1 0 1)
Atom number Structure layer Mesh of k points Surface periodicity Vacuum thickness A (Å) Vacuum thickness B (Å) Slab thickness (Å) Surface areas (Å2)
12/48/108 – 222 – – – – –
Es (A) (J/m2) Es (B) (J/m2) Es (J/m2) [37]
– – –
72 6 441 22 8.9 10 10.7 79.4 0.50 0.50 0.49
(0 0 1) 72 6 441 22 8.6 10 14.4 58.8 0.97 0.96 0.98
(1 0 0) 72 6 441 21 9.6 11 11.5 73.8 0.57 0.56 0.58
(1 0 3) 72 6 441 21 9.8 11 14.8 57.5 0.91 0.90 0.90
Fig. 2. Three configurations for a N interstitial atom in bulk anatase. The upper figures are the top view of the configurations and the the bottom ones are the side view. The gray circles represent Ti atoms, the red ones are O atoms, and the blue one is the N interstitial atom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Possible diffusion paths in bulk anatase.
unit is a distorted octahedron structure. Since in the interstitial type 1, the N atom shares one site with an oxygen atom, the N interstitial atom can diffuse from one oxygen site to another neighbor equivelent site. Due to the symmetry, there are three different O–O edges in one TiO6 octahedron structure (see Fig. 3). For example, the N interstitial atom can diffuse along three edges, the path A, B, and C in Fig. 3. The three diffusion paths and corresponding energy barriers for a N atom diffusion along three different edges are shown in Fig. 4. The diffusion barrier for the three paths are: EA = 1.43 eV, EC = 1.83 eV, and EB = 1.94 eV. In these three paths, the energy barrier for path A is at least 0.4 eV lower than that of path C and path B. Consequently, the N interstitial atom diffusion along path A is relatively easier than the diffusion along the other two directions. If an interstitial N atom diffuses in the bulk anatase continuously along a series of path A, the N atom can travel in the solid. With the combination of a series of path A, the N atom can diffuse in the direction of [1 0 0] and [0 1 0] (see Fig. 5) along the zigzag paths. Since an interstitial site is close to an oxygen atom, the zigzag path is represented by the connection of a series of oxygen atoms in Fig. 5. The interstitial N atom can diffuse in the direction of [1 0 0] and [0 1 0] with the diffusion barrier of 1.43 eV. With the combination of the two directions, the N atom can travel in the bulk anatase.
Fig. 5. Multiple diffusion steps of an interstitial N atom in TiO2 anatase solid along the type A path in Fig. 4.
4. N atom diffusion into the anatase surfaces 4.1. Formation energies of a N interstitial atom near the anatase surfaces In bulk anatase, a N interstitial atom stays at a position in the type 1 configuration (see Fig. 2). Near the surface area, serious configuration distortion happens after relaxation due to the interstitial atom. The N interstitial atom formation energies near the anatase surface area are listed in Table 2. In this table, a subscript ‘o’ is used for the serious distorted interstitial configurations. Super cells in Fig. 1 are used to study the N atom diffusion into the anatase surfaces. The interstitial sites studied in this work in each cell are denoted as ‘‘1, 2, 3, . . . ’’ in Fig. 1 and ‘‘O1, O2, O3, . . .’’ in Table 2. The data in Table 2 shows that the formation energy for a N interstitial atom increases with the depth, that is the distance from the interstitial atom to the surface. It suggests that it is difficult for an interstitial N atom diffusing into the deeper sites from the surfaces. In the super cells for (1 0 0) and (1 0 1) surface calculations, the interstitial formation energies at deep sites are close to that of the bulk, which is 1.145 eV. So, the surface effect is mainly located at the top two or three structure layers. When a N atom diffuses into deep sites, the environment for this atom is close to that of the bulk. For the N atom diffusing into the bulk from a surface, it
(b) (a)
Fig. 4. (a) Three non-equivalent diffusion paths along the three edges of the distorted octahedron in Fig. 3. (b) Diffusion barriers for the three diffusion paths. The Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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X. Hu et al. / Computational Materials Science 82 (2014) 107–113 Table 2 The formation energies of a N interstitial atom near the anatase surfaces. Subscript ‘o’ means serious configuration distortion happens after relaxation for the N interstitial structure. The unit of energy is eV. (1 0 1)
(0 0 1)
(1 0 0)
(1 0 3)
Site
Energy
Site
Energy
Site
Energy
Site
Energy
O7(o) O2(o) O3(o) O4 O1 O5 O6
2.714 2.074 1.564 1.503 1.147 1.143 1.120
O2(o) O1(o) O5 O6 O3 O4
3.199 1.933 1.093 0.918 0.916 0.741
O1(o) O2(o) O5 O3 O6 O4
2.553 2.293 1.402 1.236 1.211 1.178
O2(o) O8(o) O9(o) O1(o) O5 O4 O7 O10 O6 O3
3.249 2.935 2.154 1.987 1.250 1.222 1.213 1.097 1.089 0.912
has to go cross the outmost surface regime (about two or three structure layers) and then go into the bulk. The diffusion paths and corresponding barriers for different surfaces are different. Consequently, the surface diffusion barriers for a N atom is interesting and the diffusion barriers for different surfaces can tell us which surface is the better one for the N doping processes. 4.2. A nitrogen atom diffusing into the bulk from anatase (1 0 1) surface via interstitial sites Nitrogen interstitial atom diffusion into the bulk from an anatase (1 0 1) surface is studied in this section. The super cell used to simulate the diffusion process is shown in Fig. 1(a). Since a N interstitial atom share a lattice with an oxygen atom, the position of the oxygen atoms are used to describe the possible interstitial position in the super cell. In this super cell, the site 2, 3, and 7 are at the outermost surface of the super cell. Interstitial site 1 is a subsurface site. Site 4, 5, and 6 are at even deeper position in the super cell. The process of a nitrogen atom diffusing into the bulk from the surface is studied and the diffusion barriers are listed in Table 3. The following diffusion paths have been calculated: O2 ? O4 (from the interstitial site O2 to site O4); O3 ? O4; {O2, O3, O7} ? O1, it means the N interstitial atom can diffuse from O2, O3, or O7 to O1 position; O1 ? {O4n, O5, O6} (O4n is an O4 site in the next period along x axes). These diffusion paths and barriers show us how a nitrogen atom diffuses into the bulk from a (1 0 1) anatase surface. Energy barriers for the (1 0 1) surface diffusion are shown in Table 3. In these paths, the barrier for O3 ? O4 is the lowest one, which is 1.80 eV. The configuration and the barrier for this path is close to the diffusion path C in the bulk (see Fig. 4). The barrier is higher than that of the path A in the bulk. Although a N interstitial atom can diffuse from O2, O3, or O7 to O1 site and then diffuse to O4, the barriers for the interstitial atom diffusing to the O1 site are much higher and they are not efficient diffusion pathways. As a
Table 3 Energy barriers for a N interstitial atom diffusing into the bulk from the (1 0 1) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier.
Fig. 6. Schematic of a N interstitial atom diffusing from site O3 to site O4 in (1 0 1) direction. The configurations of O3, O4, and the transition state are shown in the figure. Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atom is the blue one. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
result, a N interstitial atom can most likely diffuse from the pathway O3 ? O4 (see Fig. 6). For this diffusion path, the barrier is very close to the reverse diffusion barrier. Meanwhile, if a N atom diffuses to the O1 site from the surface, the reverse barriers are much lower than the counterparts. It suggests that the N atom may diffuse outside from these diffusion pathways. 4.3. A nitrogen atom diffusing into the bulk from anatase (0 0 1) surface via interstitial sites In the super cell for (0 0 1) surface diffusion calculation (see Fig. 1), sites 1 and 2 are on the outermost surface, sites 3 and 4 are the sub-surface interstitial positions, sites 5 and 6 are in the bulk. Three paths are used to study the N interstitial from the outermost surface to the sub-surface site: O1 ? O3, O1 ? O4, and O2 ? O4. Since the system energy difference for the configuration O2 and O4 is 2.44 eV, the barrier will be higher than that. The barrier for this path will be too high to be useful. For the path O1 ? O4, there is a local minimal O4a, this path can be separated into two parts: O1 ? O4a, O4a ? O4. From the subsurface to the bulk, there are three paths are studied: O3 ? O5, O3 ? O6, and O4 ? O6. The diffusion barriers are listed in Table 4. The schematic of the diffusion path O1 ? O4 ? O6 is shown in Fig. 7. The highest energy barrier is 2.28 eV in this path, which is higher than the barrier of mode A, B, and C in bulk. The first barrier is still higher than the next step and a N interstitial atom will diffuse outside easier. How a N interstitial atom diffuses into the subsurface from the outermost surface is the most difficult step for the doping process. 4.4. A nitrogen atom diffusing into the bulk from anatase (1 0 0) surface via interstitial sites In the super cell for (1 0 0) surface diffusion calculation (see Fig. 1), the sites 1 and 2 are on the surface, the sites 3 and 4 are
Table 4 Diffusion barriers for a nitrogen atom into the bulk from a (0 0 1) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier for a diffusion process.
Path
Eb1 (eV)
Eb2 (eV)
O2 ? O4 O3 ? O4
2.72 1.80
2.15 1.74
Path
Eb1 (eV)
Eb2 (eV)
O2 ? O1 O3 ? O1 O7 ? O1
2.78 2.48 2.95
1.85 2.06 1.38
O1 ? O3 O1 ? O4a O4a ? O4
2.71 2.28 0.40
1.69 1.31 0.10
O1 ? O4n O1 ? O5 O1 ? O6
1.57 1.89 2.17
1.70 1.88 2.15
O3 ? O5 O3 ? O6 O4 ? O6
1.76 0.83 1.78
1.94 0.83 1.96
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Fig. 7. Schematic of a N interstitial atom diffusion via path O1 ? O4 ? O6 on an anatase (0 0 1) surface. The configurations of O1, O4, O6, and the transition states are shown in the figure. Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
at sub-surface position, and the sites 5 and 6 are in the bulk. The diffusion barriers for six paths are calculated and they are listed in Table 5. The barriers for the paths O1 ? O4, O1 ? O3, and O2 ? O4 are higher than 2.38 eV. Meanwhile, the barriers for the paths O4 ? O5, O3s ? O5, O4 ? O6 are lower than 1.80 eV. Near site O3, there is a local minimal in the path O3 ? O5. Since the barrier of the diffusion O3 ? O3s is very low, the barrier of the path O3s ? O5 is used to evaluate the barrier of O3 ? O5. It suggests that if a nitrogen atom diffuses into the bulk from a (1 0 0) surface, the first step is more difficult than the second step since the barriers of the first step are higher than that of the second step and the barrier of bulk diffusion. In the first step, the barriers are much lower than that of the reverse barriers. As a result, for the N doping process via (1 0 0) surface, the outermost diffusion step is the most difficult. On the other hand, the N interstitial will diffuse outside to the surface easily. The schematic of the diffusion path O1 ? O4 ? O5 is shown in Fig. 8. For the second step, the barriers are lower than that of the reverse barriers. So, once a N atom diffuses to a subsurface Table 5 Diffusion barriers for a nitrogen atom diffusion into the bulk from a (1 0 0) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier for a diffusion process. Path
Eb1 (eV)
Eb2 (eV)
O1 ? O4 O1 ? O3 O2 ? O4
2.38 2.74 2.71
1.01 1.43 1.60
O4 ? O5 O3s ? O5 O4 ? O6
1.06 1.62 1.76
1.28 1.72 1.89
position, it is relatively easy for this atom to diffuse to the bulk. For example, if a N atom is at the site O4, the barrier for the diffusion process O4 ? O1 is 1.01 eV, and the barrier for the path O4 ? O5 is 1.06 eV. The possibilities for both side diffusion are almost the same. Once a N atom at site O4 diffuses to site O5, the reverse barrier will be higher. It can continue to diffuse into the bulk. 4.5. A nitrogen atom diffusing into the bulk from anatase (1 0 3) surface via interstitial sites In the super cell for (1 0 3) surface diffusion calculation (see Fig. 1), the sites 2 and 8 are on the outermost surface, sites 1, 3, and 9 are for the sub-surface interstitial, sites 4, 5, 6, 7, and 10 are in the bulk. Two diffusion paths are studied for the surface to subsurface diffusion: O2 ? O1 and O8 ? O9. Four paths are chosen to describe how a nitrogen interstitial atom diffuses from a sub-surface site to the bulk: O1 ? O7, O1 ? O10, O9 ? O4, and O9 ? O5.
Table 6 Energy barriers for a N interstitial atom diffusing into an anatase (1 0 3) surface. Eb1 is the diffusion barrier and Eb2 is the reverse barrier. Path
Eb1 (eV)
Eb2 (eV)
O2 ? O1 O8 ? O8a O8a ? O9a O9a ? O9
2.41 1.11 2.15 0.48
1.15 0.61 1.36 1.00
O1 ? O7 O1 ? O10 O9 ? O4 O9 ? O5a
2.66 2.43 2.29 2.69
1.89 1.31 1.35 1.79
Fig. 8. The schematic of a N atom diffusing into the bulk via a (1 0 0) surface. The diffusion path is O1 ? O4 ? O5. Three interstitial sites and two transition states (TS) are shown in the picture. The Ti atoms are the gray circles, O atoms are the red ones, the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
X. Hu et al. / Computational Materials Science 82 (2014) 107–113
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Fig. 9. The schematic of a N atom diffusing into the bulk from a (1 0 3) surface. The diffusion path is O8 ? O9 ? O4. Three interstitial sites and two transition states (TS) are shown in the picture. The Ti atoms are the gray circles, O atoms are the red ones, and the interstitial N atoms are the blue ones. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The diffusion barriers for these paths from NEB calculations are listed in Table 6. When we calculated the N interstitial diffusion via the path O8 ? O9, two local minimal configurations are found, O8a and O9a. From the diffusion barrier table, it shows that the highest barrier is 2.15 eV for this path, which is much higher than the diffusion barrier in the bulk. Similarly, the barriers are higher than the reverse barrier for the partial diffusion O8a ? O9a. The barrier for the path O2 ? O1 is 2.41 eV and it is also higher than the reverse barrier. So, a nitrogen atom diffusing into the bulk from the outermost surface is also difficult via a (1 0 3) surface. Once a nitrogen atom is at the subsurface position of a (1 0 3) surface, it can continue to diffuse to next step towards the bulk. For this step, the barriers are also higher than 2 eV and they are much higher than the corresponding reverse barriers (see Table 6). As a result, when a nitrogen atom diffuses from an outermost (1 0 3) surface, the first two steps are difficult and the N atom prefers to diffuse out of the surface. The schematic of a N atom multiple step diffusion from a (1 0 3) surface is shown in Fig. 9. The diffusion path O8 ? O9 ? O4. It seems N atom diffusion into the bulk via an (1 0 3) surface is more difficult than the reverse diffusion. 5. Conclusions For N interstitial atom diffusion in anatase bulk, the N atom may diffuse in two directions: [1 0 0]-Z path and [0 1 0]-Z path or combination of the two directions (see Fig. 5). From the surface diffusion barrier calculations, for a N interstitial atom diffusion from the outermost surface to bulk, how a N atom diffusing from the outermost surface to the sub-surface is the most difficult step. For the four surfaces we have studied, the sequence for the highest barriers for each surface is: (1 0 1) (1.80 eV) < (0 0 1) (2.28 eV) (1 0 3) (2.29 eV) < (1 0 0) (2.38 eV). It suggests that (1 0 1) surface may be the easiest one for us to dope N atom to anatase bulk from the surfaces. The (1 0 0) surface is the relatively difficult one. Meanwhile, N interstitial atoms can diffuse to the surface from the bulk easier than the diffusion in the opposite direction. Another conclusion is that if we have already synthesized some N-doped anatase particles or bulk materials, the N doping concentration near the surfaces is higher than that of the bulk. Acknowledgments This work is supported by the Chinese National Basic Research Program (973 Program) Project 2009CB939705 and the Chinese
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